In variance-scaled comparative trial S211-0, running D'Alembert against Flat Betting for 288 hands of 4-Shoe Chop (chop) on 160 units charts 6.12u vs 3.17u in expected toll and 20.11% vs 9.92% ruin under a 100-unit pit limit. Because every 8-deck coup is statistically independent under 5% Banker Commission (0.95:1) (1.0579% edge), progression rules alter drawdown speed and table-cap collisions without changing per-hand expectation.
Reference 8-deck shoe for Stress Cell S211 (D'Alembert vs Flat Betting, Four-Shoe Alternating Sawtooth under 5% Banker Commission). Big Road shows Banker (red) and Player (blue); derived roads track symmetry.
This bead is at Row 3. Column 1 stopped at Row 2, one row above → blue (≠).
Common table reading watchout: Thinking "no bead at this row" means blue. It is blue only when Column 1 stopped exactly one row above this bead.
This bead is at Row 3. Column 1 stopped at Row 2, one row above → blue (≠).
Common table reading watchout: Thinking "no bead at this row" means blue. It is blue only when Column 1 stopped exactly one row above this bead.
Column 4 has 2 beads. Column 1 has 2 beads. Same depth → red (=).
Common table reading watchout: Comparing the wrong columns. Compare Column 4, the one that just finished, with Column 1.
Stress cell S211 compares +1 on loss / -1 on win against 1-1-1-1 constant unit over 288 hands.
Probability of exhausting the 160-unit bankroll under a 100-unit house bet limit.
Theoretical erosion under 5% Banker Commission (0.95:1) (1.0579% house edge) across 288 coups.
Deepest unit trough triggered by a 3-hand run inside the chop shoe profile.
Reflects 9.38% tie frequency (27 pushes) and 2.94u in vigorish friction.
Under 4-Shoe Chop (1.0579% effective edge), combinatorial stress run S211-1 over 288 hands and a 160-unit treasury inspects a -21u drawdown (20.11% ruin) for D'Alembert Pyramid against -10u (9.92% ruin) for Flat 1-Unit Baseline inside a 100-unit cap.
In session-bounded comparative trial S211-2, running D'Alembert against Flat Betting for 288 hands of 4-Shoe Chop (chop) on 160 units documents 6.12u vs 3.17u in expected toll and 20.11% vs 9.92% ruin under a 100-unit pit limit.
| S211 exposure | D'Alembert | Flat Betting |
|---|---|---|
| D'Alembert / Flat Betting Rule | +1 on loss / -1 on win | 1-1-1-1 constant unit |
| 288-Hand Ruin (160u) | 20.11% | 9.92% |
| 4-Shoe Chop Hold (1.0579%) | 6.12u | 3.17u |
| 3-Run Trough (100u Cap) | -21u | -10u |
Under 4-Shoe Chop (1.0579% effective edge), asymmetric stress run S211-3 over 288 hands and a 160-unit treasury audits a -21u drawdown (20.11% ruin) for D'Alembert Pyramid against -10u (9.92% ruin) for Flat 1-Unit Baseline inside a 100-unit cap.
In finite-shoe comparative trial S211-4, running D'Alembert against Flat Betting for 288 hands of 4-Shoe Chop (chop) on 160 units profiles 6.12u vs 3.17u in expected toll and 20.11% vs 9.92% ruin under a 100-unit pit limit.
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